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    The University of the State of New York

    REGENTS HIGH SCHOOL EXAMINATION

    GEOMETRYWednesday, August 17, 2011 8:30 to 11:30 a.m., onlyStudent Name: ______________________________________________________________

    School Name: _______________________________________________________________

    Print your name and the name of your school on the lines above. Then turn tothe last page of this booklet, which is the answer sheet for Part I. Fold the last pagealong the perforations and, slowly and carefully, tear off the answer sheet. Then fillin the heading of your answer sheet.

    This examination has four parts, with a total of 38 questions. You must answerall questions in this examination. Write your answers to the Part I multiple-choicequestions on the separate answer sheet. Write your answers to the questions inParts II, III, and IV directly in this booklet. All work should be written in pen, exceptgraphs and drawings, which should be done in pencil. Clearly indicate the necessarysteps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

    The formulas that you may need to answer some questions in this examinationare found at the end of the examination. This sheet is perforated so you may removeit from this booklet.

    Scrap paper is not permitted for any part of this examination, but you may use

    the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graphpaper is provided at the end of this booklet for any question for which graphing maybe helpful but is not required. You may remove this sheet from this booklet. Any

    work done on this sheet of scrap graph paper will notbe scored.

    When you have completed the examination, you must sign the statement printedat the end of the answer sheet, indicating that you had no unlawful knowledge of thequestions or answers prior to the examination and that you have neither given norreceived assistance in answering any of the questions during the examination. Youranswer sheet cannot be accepted if you fail to sign this declaration.

    The use of any communications device is strictly prohibited when taking thisexamination. If you use any communications device, no matter how briefly, yourexamination will be invalidated and no score will be calculated for you.

    DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

    GEOMETRY

    GEOMETRY

    Notice

    A graphing calculator, a straightedge (ruler), and a compass must be available for you to use whiletaking this examination.

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    Geometry August 11 [2]

    Use this space forcomputations.

    Part I

    Answer all 28 questions in this part. Each correct answer will receive 2 credits. No partial creditwill be allowed. For each question, write on the separate answer sheet the numeral preceding theword or expression that best completes the statement or answers the question. [56]

    1 The statement xis a multiple of 3, andxis an even integer is truewhenxis equal to

    (1) 9 (3) 3

    (2) 8 (4) 6

    2 In the diagram below, ABCXYZ.

    A

    C

    Z

    Y

    X

    B

    Which statement must be true?

    (1) CY (3)_

    AC _YZ

    (2) AX (4)_

    CB _XZ

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    Geometry August 11 [3] [OVER]

    3 In the diagram below of ABC,_

    TV _

    BC, AT= 5, TB= 7, andAV=10.

    A

    B

    T V

    C

    What is the length of_

    VC?

    (1) 31__2 (3) 14

    (2) 71__7 (4) 24

    4 Pentagon PQRSThas_

    PQ parallel to_TS. After a translation

    of T2,5 , which line segment is parallel to_

    PQ?

    (1)

    _

    RQ (3)

    _

    TS(2)_

    RS (4)

    _

    TP

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    Geometry August 11 [4]

    5 In the diagram below of PAO,_AP is tangent to circle Oat pointA,

    OB=7, and BP=18.

    O 7 18

    A

    B P

    What is the length of_AP?

    (1) 10 (3) 17(2) 12 (4) 24

    6 A straightedge and compass were used to create the constructionbelow. Arc EFwas drawn from point B,and arcs with equal radii weredrawn from Eand F.

    B

    C

    D

    A

    E

    F

    Which statement isfalse?

    (1) mABD=mDBC

    (2) 1__2(mABC) =mABD

    (3) 2(mDBC) =mABC

    (4) 2(mABC) =mCBD

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    Geometry August 11 [5] [OVER]

    7 What is the length of the line segment whose endpoints are (1,4)and (9,2)?

    (1) 5 (3) 10

    (2) 2___17 (4) 2___26

    8 What is the image of the point (2,3) after the transformation ry-axis?

    (1) (2,3) (3) (2,3)

    (2) (2,3) (4) (3,2)

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    Geometry August 11 [6]

    9 In the diagram below, linesnandmare cut by transversalspand q.

    30

    x

    80n

    m

    pq

    Which value ofxwould make linesnandmparallel?

    (1) 110 (3) 70

    (2) 80 (4) 50

    10 What is an equation of the circle with a radius of 5 and centerat (1,4)?

    (1) (x+1)2+(y4)2=5

    (2) (x1)2+(y+4)2=5

    (3) (x+1)2+(y4)2=25

    (4) (x1)2+(y+4)2=25

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    Geometry August 11 [7] [OVER]

    11 In the diagram below of BCD, side_

    DB is extended to pointA.

    A B D

    C

    Which statement must be true?

    (1) mC>mD (3) mABC>mC

    (2) mABCmC +mD

    12 Which equation represents the line parallel to the line whose equationis 4x+2y=14 and passing through the point (2,2)?

    (1) y=2x (3) y=1__2x

    (2) y=2x+6 (4) y=1__2x+1

    13 The coordinates of pointAare (3a,4b). If pointAis the image ofpointAreflected over the liney=x, the coordinates ofAare

    (1) (4b,3a) (3) (3a,4b)

    (2) (3a,4b) (4) (4b,3a)

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    Geometry August 11 [8]

    14 As shown in the diagram below,_

    AC bisects BADand BD.

    A

    C

    DB

    Which method could be used to prove ABCADC?

    (1) SSS (3) SAS(2) AAA (4) AAS

    15 SegmentABis the diameter of circle M. The coordinates ofAare (4,3).The coordinates of Mare (1,5). What are the coordinates of B?

    (1) (6,7) (3) (3,8)

    (2) (5,8) (4) (5,2)

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    Geometry August 11 [9] [OVER]

    16 In the diagram below,_

    AB is perpendicular to planeAEFG.

    A

    B

    D

    E

    C

    G F

    H

    Which plane must be perpendicular to planeAEFG?

    (1) ABCE (3) CDFE

    (2) BCDH (4) HDFG

    17 How many points are both 4 units from the origin and also 2 unitsfrom the liney=4?

    (1) 1 (3) 3

    (2) 2 (4) 4

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    Geometry August 11 [10]

    18 When solved graphically, what is the solution to the following systemof equations?

    y=x2 4x+6

    y=x+2

    (1) (1,4) (3) (1,3) and (4,6)(2) (4,6) (4) (3,1) and (6,4)

    19 Triangle PQRhas angles in the ratio of 2:3:5. Which type of triangleis PQR?

    (1) acute (3) obtuse

    (2) isosceles (4) right

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    Geometry August 11 [11] [OVER]

    20 Plane Ais parallel to plane B. Plane Cintersects plane Ain linemandintersects plane Bin linen. Linesmandnare

    (1) intersecting (3) perpendicular

    (2) parallel (4) skew

    21 The diagonals of a quadrilateral are congruent but donotbisect eachother. This quadrilateral is

    (1) an isosceles trapezoid (3) a rectangle

    (2) a parallelogram (4) a rhombus

    22 What is the slope of a line perpendicular to the line represented bythe equationx+2y=3?

    (1) 2 (3) 1__2

    (2) 2 (4) 1__2

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    Geometry August 11 [12]

    23 A packing carton in the shape of a triangular prism is shown in thediagram below.

    What is the volume, in cubic inches, of this carton?

    (1) 20 (3) 120

    (2) 60 (4) 240

    24 In the diagram below of circle O, diameter_

    AOB is perpendicular tochord_CD at point E, OA=6, and OE=2.

    A B

    C

    D

    O E

    What is the length of_

    CE?(1) 4

    __

    3 (3) 8__

    2

    (2) 2__

    3 (4) 4__

    2

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    Geometry August 11 [13] [OVER]

    25 What is the measure of each interior angle of a regular hexagon?

    (1) 60 (3) 135

    (2) 120 (4) 270

    26 Which equation represents the perpendicular bisector of_

    ABwhoseendpoints areA(8,2) and B(0,6)?

    (1) y=2x4 (3) y=1__2x+6

    (2) y=1__2x+2 (4) y=2x12

    27 As shown in the diagram below, a kite needs a vertical and a horizontalsupport bar attached at opposite corners. The upper edges of the kiteare 7 inches, the side edges arexinches, and the vertical support baris (x+1) inches.

    7inche

    s

    xin

    ches

    (x

    +1

    )inches

    What is the measure, in inches, of the vertical support bar?

    (1) 23 (3) 25

    (2) 24 (4) 26

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    Geometry August 11 [14]

    28 Given three distinct quadrilaterals, a square, a rectangle, and arhombus, which quadrilaterals must have perpendicular diagonals?

    (1) the rhombus, only

    (2) the rectangle and the square

    (3) the rhombus and the square

    (4) the rectangle, the rhombus, and the square

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    Geometry August 11 [15] [OVER]

    Part II

    Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. All answers should be written in pen, except for graphs and drawings,

    which should be done in pencil. [12]

    29 In the diagram below, trapezoidABCD, with bases_

    AB and_

    DC, is inscribed in circle O, with

    diameter_

    DC. If mAB=80, find mBC.

    O

    80

    D

    A B

    C

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    Geometry August 11 [16]

    30 On the diagram ofABCshown below,use a compass and straightedge to construct theperpendicular bisector of

    _

    AC . [Leave all construction marks.]

    A

    C

    B

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    Geometry August 11 [17] [OVER]

    31 A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, interms of .

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    Geometry August 11 [18]

    32 Write an equation of the circle graphed in the diagram below.

    y

    x

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    Geometry August 11 [19] [OVER]

    33 The diagram below showsABC, with_

    AEB ,_

    ADC , and ACBAED. Prove thatABCis similar to ADE.

    CB

    D

    A

    E

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    Geometry August 11 [20]

    34 TriangleABChas verticesA(3,3), B(7,9), and C(11,3). Determine the point of intersection of themedians, and state its coordinates. [The use of the set of axes below is optional.]

    y

    x

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    Geometry August 11 [21] [OVER]

    Part III

    Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. All answers should be written in pen, except for graphs and drawings,

    which should be done in pencil. [12]

    35 In the diagram below of GJK, H is a point on_GJ,_HJ _JK, mG=28, and mGJK=70.

    Determine whether GHKis an isosceles triangle and justify your answer.

    G H J

    7028

    K

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    Geometry August 11 [22]

    36 As shown on the set of axes below,GHShas vertices G(3,1), H(5,3), and S(1,4). Graph and statethe coordinates of GHS, the image of GHSafter the transformation T3,1D2.

    y

    xG

    S

    H

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    Geometry August 11 [23] [OVER]

    37 In the diagram below,ABCDEF, DE=4,AB=x,AC=x+2, and DF=x+6.Determine the length of

    _

    AB. [Only an algebraic solution can receive full credit.]

    C

    B

    A

    x +6x +24

    x

    E

    F

    D

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    Part IV

    Answer the question in this part. A correct answer will receive 6 credits. Clearly indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

    A correct numerical answer with no work shown will receive only 1 credit. The answer shouldbe written in pen.[6]

    Geometry August 11 [24]

    38 Given: ABCwith verticesA(6,2), B(2,8), and C(6,2)

    _

    AB has midpoint D,_

    BC has midpoint E, and_

    AC has midpoint F

    Prove: ADEFis a parallelogram

    ADEFisnota rhombus

    [The use of the grid below is optional.]

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    TearHere

    Reference Sheet

    TearHere

    Volume

    Lateral Area (L)

    Surface Area

    Cylinder

    Pyramid

    Right Circular Cone

    Sphere

    VBh

    where Bis the area of the base

    Right Circular Cylinder

    Right Circular Cone

    Sphere

    VBh

    where Bis the area of the base

    13

    VBh

    where Bis the area of the base

    13

    Vr343

    L2rh

    SA4r2

    Lrl

    where lis the slant height

    Geometry August 11

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    Scrap Graph Paper This sheet will not be scored.

    TearHere

    TearHere

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    Scrap Graph Paper This sheet will not be scored.

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    TearHere

    TearHere

    Your answers for Parts II, III, and IV should be written in the test booklet.

    The declaration below must be signed when you have completed the examination.

    I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to theexamination and that I have neither given nor received assistance in answering any of the questions during the examination.

    Signature

    The University of the State of New York

    REGENTS HIGH SCHOOL EXAMINATION

    GEOMETRY

    Wednesday, August 17, 20118:30 to 11:30 a.m., only

    ANSWER SHEET

    Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Grade . . . . . .

    Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    Your answers to Part I should be recorded on this answer sheet.

    Part I

    Answer all 28 questions in this part.

    1 . . . . . . . . . . . . . . . .

    2 . . . . . . . . . . . . . . . .

    3 . . . . . . . . . . . . . . . .

    4 . . . . . . . . . . . . . . . .

    5 . . . . . . . . . . . . . . . .

    6 . . . . . . . . . . . . . . . .

    7 . . . . . . . . . . . . . . . .

    8 . . . . . . . . . . . . . . . .

    9 . . . . . . . . . . . . . . . .

    10 . . . . . . . . . . . . . . . .

    11 . . . . . . . . . . . . . . . .

    12 . . . . . . . . . . . . . . . .

    13 . . . . . . . . . . . . . . . .

    14 . . . . . . . . . . . . . . . .

    15 . . . . . . . . . . . . . . . .

    16 . . . . . . . . . . . . . . . .

    17 . . . . . . . . . . . . . . . .

    18 . . . . . . . . . . . . . . . .

    19 . . . . . . . . . . . . . . . .

    20 . . . . . . . . . . . . . . . .

    21 . . . . . . . . . . . . . . . .

    22 . . . . . . . . . . . . . . . .

    23 . . . . . . . . . . . . . . . .

    24 . . . . . . . . . . . . . . . .

    25 . . . . . . . . . . . . . . . .

    26 . . . . . . . . . . . . . . . .

    27 . . . . . . . . . . . . . . . .

    28 . . . . . . . . . . . . . . . .

    Geometry August 11

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    GEOMETRY

    QuestionMaximum

    CreditCreditsEarned

    Raters/ScorersInitials

    Part I 128 56

    Part II 29 2

    30 2

    31 2

    32 2

    33 2

    34 2

    Part III 35 4

    36 4

    37 4

    Part IV 38 6

    MaximumTotal

    86

    Total RawScore

    Checked by Scale Score(from conversion chart)

    Raters/Scorers Name(minimum of three)

    GEOMETRY

    GEOMETRYPrinted on Recycled Paper

    Geometry August 11

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    FOR TEACHERS ONLYThe University of the State of New York

    REGENTS HIGH SCHOOL EXAMINATION

    GEOMETRY

    Wednesday, August 17, 2011 8:30 to 11:30 a.m., only

    SCORING KEY AND RATING GUIDE

    Mechanics of Rating

    The following procedures are to be followed for scoring student answer papers for theRegents Examination in Geometry. More detailed information about scoring is provided inthe publication Information Booklet for Scoring the Regents Examinations in Mathematics.

    Do notattempt to correct the students work by making insertions or changes of any kind.In rating the open-ended questions, you may make check marks in the exam booklet toindicate student errors. If the students were given scannable answer sheets for the multiple-choice questions, be careful not to make any stray marks on the answer sheet that might laterinterfere with the accuracy of the scanning.

    Unless otherwise specified, mathematically correct variations in the answers will beallowed. Units need not be given when the wording of the questions allows such omissions.

    Each students answer paper is to be scored by a minimum of three mathematicsteachers. No one teacher is to score more than approximately one-third of the open-endedquestions on a students paper. On the back of the students detachable answer sheet, ratersmust enter their initials in the boxes next to the questions they have scored and also write their

    name in the box under the heading Raters/Scorers Name.Schools are not permitted to rescore any of the open-ended questions on this

    exam after each question has been rated once, regardless of the final exam score.Schools are required to ensure that the raw scores have been added correctly andthat the resulting scale score has been determined accurately.

    Raters should record the students scores for all questions and the total raw score on thestudents detachable answer sheet. Then the students total raw score should be converted to ascale score by using the conversion chart that will be posted on the Departments web site at:http://www.p12.nysed.gov/apda/ on Wednesday, August 17, 2011. Because scale scorescorresponding to raw scores in the conversion chart may change from one administration toanother, it is crucial that for each administration, the conversion chart provided for thatadministration be used to determine the students final score. The students scale score should

    be entered in the box provided on the students detachable answer sheet. The scale score is thestudents final examination score.

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    Geometry Rating Guide August 11 [2]

    Part I

    Allow a total of 56 credits, 2 credits for each of the following. Allow credit if the studenthas written the correct answer instead of the numeral 1, 2, 3 , or 4.

    (1) 4 (8) 2 (15) 1 (22) 2

    (2) 2 (9) 3 (16) 1 (23) 3

    (3) 3 (10) 4 (17) 2 (24) 4

    (4) 3 (11) 3 (18) 3 (25) 2

    (5) 4 (12) 2 (19) 4 (26) 1

    (6) 4 (13) 1 (20) 2 (27) 3

    (7) 3 (14) 4 (21) 1 (28) 3

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    Geometry Rating Guide August 11 [3]

    Updated information regarding the rating of this examination may be posted on the New York State Education Departmentsweb site during the rating period. Check this web site http://www.p12.nysed.gov/apda/and select the link Scoring Informationfor any recently posted information regarding this examination. This site should be checked before the rating process for thisexamination begins and several times throughout the Regents Examination period.

    General Rules for Applying Mathematics Rubrics

    I. General Principles for RatingThe rubrics for the constructed-response questions on the Regents Examination in Geometry are designed to provide asystematic, consistent method for awarding credit. The rubrics are not to be considered all-inclusive; it is impossible toanticipate all the different methods that students might use to solve a given problem. Each response must be rated carefullyusing the teachers professional judgment and knowledge of mathematics; all calculations must be checked. The specificrubrics for each question must be applied consistently to all responses. In cases that are not specifically addressed in therubrics, raters must follow the general rating guidelines in the publication Information Booklet for Scoring the RegentsExaminations in Mathematics, use their own professional judgment, confer with other mathematics teachers, and/or contactthe State Education Department for guidance. During each Regents Examination administration period, rating questions maybe referred directly to the State Education Department. The contact numbers are sent to all schools before eachadministration period.

    II. Full-Credit Responses

    A full-credit response provides a complete and correct answer to all parts of the question. Sufficient work is shown to enable

    the rater to determine how the student arrived at the correct answer.When the rubric for the full-credit response includes one or more examples of an acceptable method for solving the question(usually introduced by the phrase such as), it does not mean that there are no additional acceptable methods of arriving at thecorrect answer. Unless otherwise specified, mathematically correct alternative solutions should be awarded credit. The onlyexceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphicsolution. A correct solution using a method other than the one specified i s awarded half the credit of a correct solution usingthe specified method.

    III. Appropriate Work

    Full-Credit Responses:The directions in the examination booklet for all the constructed-response questions state: Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The student has theresponsibility of providing the correct answer and showing how that answer was obtained. The student must construct theresponse; the teacher should not have to search through a group of seemingly random calculations scribbled on the studentpaper to ascertain what method the student may have used.

    Responses With Errors:Rubrics that state Appropriate work is shown, but are intended to be used with solutions thatshow an essentially complete response to the question but contain certain types of errors, whether computational, rounding,

    graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved butnot all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incompleteresponses.

    IV. Multiple Errors

    Computational Errors, Graphing Errors, and Rounding Errors:Each of these types of errors results in a 1-credit deduction.Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted forsuch mechanical errors in any response. The teacher must carefully review the students work to determine what errors weremade and what type of errors they were.

    Conceptual Errors:A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptualerrors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, ormultiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual

    error can receive no more than half credit.If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the sameconceptual error is repeated in responses to other questions, credit should be deducted in each response.

    If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect andreceive no credit.

    If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award creditthat takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for eachmechanical error (maximum of two deductions for mechanical errors).

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    Geometry Rating Guide August 11 [4]

    Part II

    For each question, use the specific criteria to award a maximum of two credits. Unlessotherwise specified, mathematically correct alternative solutions should be awardedappropriate credit.

    (29) [2] 50, and appropriate work is shown, such as a labeled diagram.

    [1] Appropriate work is shown, but one computational error is made.

    or

    [1] Appropriate work is shown, but one conceptual error is made.

    or

    [1] 2x+ 80 = 180 or an equivalent equation is written, but no further correctwork is shown.

    or

    [1]50, but no work is shown.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct

    response that was obtained by an obviously incorrect procedure.

    (30) [2]A correct construction is drawn showing all appropriate arcs, and the

    perpendicular bisector is correctly drawn.

    [1]A correct construction is drawn showing all appropriate arcs, but the

    perpendicular bisector of AB or BCis drawn.

    or

    [1]A correct construction is drawn showing all appropriate arcs, but the

    perpendicular bisector is not drawn.

    [0] A drawing that is not an appropriate construction is shown.

    or

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [5]

    (31) [2]972, and appropriate work is shown.

    [1]Appropriate work is shown, but one computational error is made, but an

    appropriate answer is written in terms of .

    or

    [1]Appropriate work is shown, but one conceptual error is made, but an appropriateanswer is written in terms of .

    or

    [1]Appropriate work is shown, but the answer is not written in terms of .

    or

    [1]972, but no work is shown.[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct

    response that was obtained by an obviously incorrect procedure.

    (32) [2](x 5)2+ ( y+ 4)

    2= 36.

    [1]Appropriate work is shown, but one computational error is made.

    or

    [1]Appropriate work is shown, but one conceptual error is made.

    or

    [1]Center of (5, 4) and radius of 6 are stated, but no further correct work is

    shown.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct

    response that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [6]

    (33) [2] A complete and correct proof that includes a conclusion is written.

    [1]Only one correct statement and reason are written.

    or

    [1]One conceptual error is made.

    [0] The given and/or the prove statements are written, but no further correct

    relevant statements are written.

    or

    [0]A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponsethat was obtained by an obviously incorrect procedure.

    (34) [2] (7,5), and appropriate work is shown, such as locating the centroid on the

    vertical median or graphing at least two medians.

    [1]Appropriate work is shown, but one computational or graphing error is made.

    or

    [1]Appropriate work is shown, but one conceptual error is made.

    or

    [1]One or two medians are graphed correctly and the median is located, but the

    coordinates are not stated or are stated incorrectly.

    or

    [1](7,5), but no work is shown.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [7]

    Part III

    For each question, use the specific criteria to award a maximum of four credits. Unlessotherwise specified, mathematically correct alternative solutions should be awardedappropriate credit.

    (35) [4] The triangle is not isosceles, and an appropriate justification is given, suchas a correctly labeled diagram.

    [3] Appropriate work is shown, but one computational error is made, but an

    appropriate determination is made, and an appropriate justification is given.

    [2] Appropriate work is shown, but two or more computational errors are made, butan appropriate determination is made, and an appropriate justification is given.

    or

    [2]Appropriate work is shown, but one conceptual error is made, but an appropriatedetermination is made, and an appropriate justification is given.

    or

    [2]The correct measures of JHKor JKHand GKHor GHKare found, but

    no determination is made.

    [1] Appropriate work is shown, but one conceptual error and one computational

    error are made, but an appropriate determination is made, and an appropriatejustification is given.

    or

    [1]Appropriate work is shown to find the correct measure of JHKor JKH, but

    no further correct work is shown.

    [0] Indicates the triangle is not isosceles, but no work is shown.

    or

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [8]

    (36) [4]G(3,3), H(7,7), and S(1,9) are graphed, stated, and labeled correctly, andappropriate work is shown.

    [3]Appropriate work is shown, but one computational, graphing, or labeling error

    is made, but appropriate coordinates are graphed, stated, and labeled.

    or

    [3] Appropriate work is shown to find G(3,3), H(7,7), and S(1,9), but no graph

    is drawn.or

    [3] GHSis graphed and labeled correctly, but the coordinates are not stated or

    are stated incorrectly.

    [2]Appropriate work is shown, but two or more computational, graphing, or

    labeling errors are made, but appropriate coordinates are graphed, stated, and

    labeled.or

    [2]Appropriate work is shown, but one conceptual error is made, such as

    performing the translation before the dilation, but appropriate coordinates aregraphed, stated, and labeled.

    or

    [2]The dilation is performed correctly, the image is graphed and labeled correctly,

    and the coordinates are labeled and stated correctly, but no further correct workis shown.

    [1] Appropriate work is shown, but one conceptual error and one computational,

    graphing, or labeling error are made, but appropriate coordinates are graphed,stated, and labeled.

    or

    [1]Appropriate work is shown to find (3,3), (7,7), and (1,9), but the points are not

    labeled, and no graph is drawn.

    or

    [1]Appropriate work is shown to find G(6,2), H(10,6), and S(2,8), but no further

    correct work is shown.

    or

    [1] The dilation is graphed and labeled correctly, but no further correct work isshown.

    or

    [1] G(3,3), H(7,7), and S(1,9), but no work is shown, and no graph is drawn.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct

    response that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [9]

    (37) [4]2, and appropriate algebraic work is shown.

    [3]Appropriate work is shown, but one computational or factoring error is made.

    or

    [3]Appropriate work is shown, but the negative root is included in the solution.

    [2]Appropriate work is shown, but two or more computational or factoring errors are

    made.

    or

    [2]Appropriate work is shown, but one conceptual error is made.

    or

    [2] A correct quadratic equation in standard form (set equal to zero) is written, butno further correct work is shown.

    or

    [2]Work is shown to find 2, but a method other than algebraic is used.

    [1]Appropriate work is shown, but one conceptual error and one computational or

    factoring error are made.

    or

    [1] A correct proportion is written, but no further correct work is shown.

    or

    [1]2, but no work is shown.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [10]

    Part IV

    For this question, use the specific criteria to award a maximum of six credits. Unlessotherwise specified, mathematically correct alternative solutions should be awardedappropriate credit.

    (38) [6]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, and an appropriate concluding statement is made.

    [5]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but one computational or graphing error is made.

    or

    [5]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but the concluding statement is missing or is incorrect.

    [4]Appropriate work is shown to prove

    ADEF

    is a parallelogram and not arhombus, but two or more computational or graphing errors are made.

    or

    [4]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but one conceptual error is made.

    [3]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but two or more computational or graphing errors are made, and theconcluding statement is missing or is incorrect.

    or

    [3]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but one conceptual error and one computational or graphing error aremade.

    or

    [3]Appropriate work is shown to prove ADEFis a parallelogram, but no furthercorrect work is shown.

    or

    [3]Appropriate work is shown to prove ADEFis not a rhombus, but no furthercorrect work is shown.

    [2]Appropriate work is shown to prove ADEFis a parallelogram and not arhombus, but two conceptual errors are made.

    or

    [2]Appropriate work is shown to prove DE||AFand

    AD ||

    FE, but no further

    correct work is shown.

    or

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    Geometry Rating Guide August 11 [11]

    [2]Appropriate work is shown to prove that DFand AEbisect each other, but no

    further correct work is shown.

    or

    [2]Appropriate work is shown to prove that DFis not perpendicular toAE, but no

    further correct work is shown.

    or

    [2]Appropriate work is shown to find the lengths of all four sides, but no further

    correct work is shown.

    or

    [2] Appropriate work is shown to prove one pair of opposite sides are bothcongruent and parallel, but no further correct work is shown.

    [1]Appropriate work is shown to find the midpoints of DFandAE, but no further

    correct work is shown.

    or

    [1]Appropriate work is shown to find all four slopes, but no further correct work is

    shown.

    or

    [1] Midpoints D, E, and Fare found, but no further correct work is shown.

    [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.

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    Geometry Rating Guide August 11 [12]

    Map to Core Curriculum

    Content Band Item Numbers

    Geometric Relationships 16, 20, 23, 31

    Constructions 6, 30

    Locus 17, 34

    Informal and Formal Proofs1, 2, 3, 5, 9, 11, 14, 19, 21, 24, 25, 27,

    28, 29, 33, 35, 37

    Transformational Geometry 4, 8, 13, 36

    Coordinate Geometry 7, 10, 12, 15, 18, 22, 26, 32, 38

    Regents Examination in GeometryAugust 2011

    Chart for Converting Total Test Raw Scores toFinal Examination Scores (Scale Scores)

    The Chart for Determining the Final Examination Score for the August 2011Regents Examination in Geometrywill be posted on the Departments web site at:http://www.p12.nysed.gov/apda/ on Wednesday, August 17, 2011. Conversioncharts provided for previous administrations of the Geometry examination mustNOT be used to determine students final scores for this administration.

    Online Submission of Teacher Evaluations of the Test to the Department

    Suggestions and feedback from teachers provide an important contribution to the testdevelopment process. The Department provides an online evaluation form for Stateassessments. It contains spaces for teachers to respond to several specific questions and to makesuggestions. Instructions for completing the evaluation form are as follows:

    1. Go to http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm.

    2. Select the test title.

    3. Complete the required demographic fields.

    4. Complete each evaluation question and provide comments in the space provided.

    5. Click the SUBMIT button at the bottom of the page to submit the completed form.

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    Regents Examination in GeometryAugust 2011

    Chart for Converting Total Test Raw Scores toFinal Examination Scores (Scale Scores)

    RawScore

    ScaleScore

    RawScore

    ScaleScore

    RawScore

    ScaleScore

    RawScore

    ScaleScore

    86 100 64 79 42 66 20 43

    85 98 63 78 41 65 19 41

    84 97 62 78 40 64 18 39

    83 95 61 77 39 64 17 38

    82 94 60 77 38 63 16 36

    81 93 59 76 37 62 15 34

    80 92 58 75 36 61 14 32

    79 90 57 75 35 60 13 30

    78 89 56 74 34 59 12 28

    77 88 55 74 33 58 11 26

    76 87 54 73 32 58 10 24

    75 86 53 73 31 57 9 22

    74 86 52 72 30 55 8 19

    73 85 51 72 29 54 7 17

    72 84 50 71 28 53 6 15

    71 83 49 70 27 52 5 12

    70 83 48 70 26 51 4 10

    69 82 47 69 25 50 3 7

    68 81 46 69 24 48 2 5

    67 81 45 68 23 47 1 2

    66 80 44 67 22 46 0 065 79 43 67 21 44

    To determine the students final examination score, find the students total test rawscore in the column labeled Raw Score and then locate the scale score thatcorresponds to that raw score. The scale score is the students final examination score.Enter this score in the space labeled Final Score on the students answer sheet.

    Schools are not permitted to rescore any of the open-ended questions on thisexam after each question has been rated once, regardless of the final exam score.

    Schools are required to ensure that the raw scores have been added correctlyand that the resulting scale score has been determined accurately.

    Because scale scores corresponding to raw scores in the conversion chart change fromone administration to another, it is crucial that for each administration the conversionchart provided for that administration be used to determine the students final score.